Field Theory Entropy, the $H$-theorem and the Renormalization Group

TL;DR

This paper explores entropy and relative entropy in field theory, demonstrating their monotonic behavior under renormalization group flows and proposing relative entropy as a measure that increases across fixed points in higher dimensions.

Contribution

It establishes the monotonicity of entropy and relative entropy in field theories under RG flows and introduces relative entropy as a natural measure increasing between fixed points.

Findings

Relative entropy ranks fixed points in field theory.

Wilsonian RG flows increase entropy in the system.

Relative entropy increases from one fixed point to another in higher dimensions.

Abstract

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized $H$ theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions.